elementaryQuotient(...,CheckWellDefined=>...) -- check whether the list is a modular cut or linear subclass

Synopsis

• Usage:

  elementaryQuotient(M, L, CheckWellDefined => true)

• Inputs:
  • M, a matroid
  • L, a list, a list of flats or hyperplanes of the matroid forming a modular cut/linear subclass
• Outputs:
  • a matroid, the elementary quotient of the matroid associated to modular cut/linear subclass

Description

This option is provided by the package Matroids.

When producing the elementary quotient of a matroid M corresponding to a list of flats or hyperplanes L, setting this option to true calls isModularCut or isLinearSubclass to check that the list is a modular cut or linear subclass respectively.

i1 : A = matrix {{1, 0, 0, 1, 1}, {0, 1, 0, 1, -1}, {0, 0, 1, 0, 0}}

o1 = | 1 0 0 1 1  |
     | 0 1 0 1 -1 |
     | 0 0 1 0 0  |

              3       5
o1 : Matrix ZZ  <-- ZZ

i2 : M = matroid A

o2 = a "matroid" of rank 3 on 5 elements

o2 : Matroid

i3 : K = modularCut(M, drop(hyperplanes M, 1))

o3 = {set {2}, set {4, 2}, set {2, 3}, set {1, 2}, set {0, 2}, set {0, 1, 2,
     ------------------------------------------------------------------------
     3, 4}}

o3 : List

i4 : elementaryQuotient(M, K, CheckWellDefined => true)

o4 = a "matroid" of rank 2 on 5 elements

o4 : Matroid

Further information

• Default value: false
• Function: elementaryQuotient -- associated to a modular cut or linear subclass
• Option key: CheckWellDefined -- an optional argument

See also

• elementaryQuotient -- associated to a modular cut or linear subclass

Functions with optional argument named CheckWellDefined :

• relaxation(...,CheckWellDefined=>...) -- see CheckWellDefined -- an optional argument
• elementaryQuotient(...,CheckWellDefined=>...) -- check whether the list is a modular cut or linear subclass
• extension(...,CheckWellDefined=>...) -- check whether the list is a modular cut or linear subclass
• linearSubclass(...,CheckWellDefined=>...) -- check whether the list is a modular cut
• modularCut(...,CheckWellDefined=>...) -- check whether the list is a linear subclass